Let $z_1, z_2 \in \mathbb{C}$ such that $|z_1 + z_2| = \sqrt{3}$ and $|z_1| = |z_2| = 1$. Then the value of $|z_1 - z_2|$ is

If $z=x+iy$ is a complex number satisfying $\left|z+\frac{i}{2}\right|^2=\left|z-\frac{i}{2}\right|^2$,then the locus of $z$ is

The locus of $z=x+iy$, such that $\operatorname{Im}\left(\frac{z-3i}{iz+4}\right)=0$ is

If $|z + 4| \le 3$,then the maximum value of $|z + 1|$ is

The equation $|z+1-i|=|z-1+i|$ represents a (where $z$ is a complex number)

Let $C$ be the set of all complex numbers. Let $S_{1}=\{z \in C:|z-2| \leq 1\}$ and $S_{2}=\{z \in C: z(1+i)+\overline{z}(1-i) \geq 4\}$. Then,the maximum value of $\left|z-\frac{5}{2}\right|^{2}$ for $z \in S_{1} \cap S_{2}$ is equal to: